Let us consider the junction conditions
for the smooth matching of the interior manifold \(\mathcal {M^-}\)  (equation (REF ) considered above)
with the exterior manifold \(\mathcal {M^+}\)  across timelike hypersurface \(\Sigma \) ,
at \(r=r_b\) . As described in [1]}, [2]}, the junction conditions for the \(f(R)\)  gravity
requires the matching of several geometric quantities other than
the induced metric (\(h_{ij}\) ) and the extrinsic curvature (\(K_{ij})\) .
In fact, it has been established that in
\(f(R)\)  gravity, the following variables must be matched at the boundary:
\([h_{ij}]_{-}^{+}&=&0, \\F(R)\,[K_{ij}-(1/3)K\, h_{ij}]_{-}^{+}&=&0, \\~[K]_{-}^{+}&=&0, \\(\partial F(R)/ \partial R)\,[\partial _{\tau }R]_{-}^{+}&=&0, \\~[R]_{-}^{+}&=&0,\) 
